There are many and varied requirements for performing multiplication procedures on extremely complicated and complex mathematical expressions. Such multiplication facilitates studies and analyses such as analysis in the frequency domain, for example, which is often desired.
In many methods of analysis there is a requirement for producing linear transforms, one of the most common examples of which is the requirement for the production of a Fourier transform. In older prior art procedures such linear transforms were produced by laborious mathematical procedures carried out by a series of lengthy, complex, and detailed individual mathematical computations.
More recently, however, the electronic data processing and computation arts have progressed to a point which enables the completion of such mathematical computations by electronic data processing and computation equipments.
The adaptation of optical techniques has many advantages including ease of recording such as on a photographic film, for example, by reason of which degrees of opacity (or conversely degrees of transmittance) are readily made to represent predetermined mathematical values. Moreover, optical techniques facilitate the ready substitution of such recorded information and make use as well of the readily available capabilities of the modern electronic optical arts including those attributes exhibited by light emitting devices, such as light emitting diodes, and the desirable aspects of a light responsive equipment, such as a photo-responsive charge coupled array.
Accordingly, it is desirable that the advantageous aspects of electro optical techniques be availed of to perform mathematical computations such as matrix-vector multiplication to produce linear transforms.